Constant of Proportionality (tables, graphs, word problems)

Front

What is the Constant of Proportionality?

Back

The Constant of Proportionality is the ratio between two proportional quantities, often represented as 'k'. It remains constant as the values change.

Front

How do you find the Constant of Proportionality from a table?

Back

To find the Constant of Proportionality from a table, divide the value of one quantity by the corresponding value of the other quantity. If the ratio is the same for all pairs, that ratio is 'k'.

Front

What does a graph of a proportional relationship look like?

Back

A graph of a proportional relationship is a straight line that passes through the origin (0,0). The slope of the line represents the Constant of Proportionality.

Front

If a car travels 90 miles in 2 hours, what is the Constant of Proportionality?

Back

The Constant of Proportionality is 45 miles per hour (90 miles ÷ 2 hours = 45 miles/hour).

Front

What is the formula to calculate the Constant of Proportionality?

Back

The formula is k = y/x, where 'y' is the dependent variable and 'x' is the independent variable.

Front

If the Constant of Proportionality is 15, what does this mean in a word problem context?

Back

It means that for every unit increase in the independent variable, the dependent variable increases by 15 units.

Front

How can you determine if two quantities are proportional?

Back

Two quantities are proportional if their ratios are constant, meaning the Constant of Proportionality is the same for all pairs of values.

Front

What is an example of a real-world situation that involves the Constant of Proportionality?

Back

An example is the relationship between distance and time when driving at a constant speed. The speed is the Constant of Proportionality.

Front

If a recipe calls for 2 cups of flour for every 3 cups of sugar, what is the Constant of Proportionality?

Back

The Constant of Proportionality is 2/3, meaning for every 2 cups of flour, there are 3 cups of sugar.

Front

What happens to the Constant of Proportionality if the relationship is not proportional?

Back

If the relationship is not proportional, the Constant of Proportionality does not exist, as the ratio between the quantities will vary.